I'm with others. Locate it outside, or somewhere where the noise will not
be an issue.

I live in an apartment and do have a balcony, but relocating the
compressor out there is not really a viable option.

The compressor is a Senco PC1010 which is pretty small, so I may be
able to get away with rubber baffles and reasonably quiet fans to
input and output air flow. Hmmm, guess I have some things to consider.